I had all 4 of my wisdom teeth out, and only one needed a drill, and was done by a general dentist. The next 3 were done by an oral surgeon, and no drilling was needed, just the local, and expert pulling, so not loud at all.
Foam earplugs and dentistry definitely make things louder via occlusion effect. Some wear noise canceling headphones and say it helps, although I have no direct experience.
I recently had both ultrasonic tooth cleaning, and a larger cavity drilled and filled on 2 separate visits. Neither spiked my tinnitus or effected it in any way. I did notice the dental office had a lot of newer equipment, and the drill was definitely quieter than I would expect. I think some new electric drills can be a lot quieter so you can seek that out, and not sure if that is what was used on me.